“My birthday was yesterday — longest birthday ever. Started in New York, flew to L.A. and the day didn’t end and it was fantastic,” he shared. “I got nice presents and they took me out and they sang to me.”

“I need a man cave,” Fallon tells PEOPLE. “I got a truck — that was a big thing for me. I mean, don’t I look like a truck driver?”

The truck, which Fallon describes as “bigger than my first apartment in New York City,” is only partly the man cave on wheels that he envisioned it would be. “I have the backseats with two baby seats,” Fallon says.

“I thought I’d never be that annoying person [who shares pictures of his kids], but as soon as Winnie was born, I was showing iPhone snaps to a cab driver,” the Tonight Show host, 40, says in a new interview with Parents.

Of course, there are some not-so-fun things about being a dad to daughters Frances Cole, 5 months and Winnie Rose, 22 months.

“They vomit a lot. For a second I thought I needed to rename my first Linda Blair and hire a priest, because she was spitting up so much,” Fallon jokes.

But overall, the Saturday Night Live alum has taken to fatherhood like a champ.